Multiplying and Dividing Fractions

Multiplying Fractions

Multiply numerator × numerator and denominator × denominator:

$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$

Example: $\frac{2}{3} \times \frac{4}{5} = \frac{8}{15}$

Simplify Before Multiplying (Cross-Cancel)

$\frac{3}{4} \times \frac{8}{9}$

Cancel the 3 and 9 (divide by 3): $\frac{1}{4} \times \frac{8}{3}$ Cancel the 4 and 8 (divide by 4): $\frac{1}{1} \times \frac{2}{3} = \frac{2}{3}$

Multiplying Mixed Numbers

Convert to improper fractions first:

$2\frac{1}{3} \times 1\frac{1}{2} = \frac{7}{3} \times \frac{3}{2} = \frac{21}{6} = \frac{7}{2} = 3\frac{1}{2}$

Dividing Fractions

To divide by a fraction, multiply by the reciprocal (flip the second fraction):

$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$

Keep, Change, Flip!

$\frac{3}{4} \div \frac{2}{5} = \frac{3}{4} \times \frac{5}{2} = \frac{15}{8} = 1\frac{7}{8}$

What Division Means

$\frac{3}{4} \div \frac{1}{2}$ means: "How many halves fit in $\frac{3}{4}$?"

Answer: $\frac{3}{4} \div \frac{1}{2} = \frac{3}{4} \times \frac{2}{1} = \frac{6}{4} = 1\frac{1}{2}$ halves

Word Problems

A recipe calls for $\frac{3}{4}$ cup of flour. You want to make $\frac{1}{2}$ the recipe. How much flour?

$\frac{1}{2} \times \frac{3}{4} = \frac{3}{8}$ cup of flour

Remember: "Of" means multiply! "$\frac{1}{2}$ of $\frac{3}{4}$" = $\frac{1}{2} \times \frac{3}{4}$